SSC CPO SI and ASI 2014 Paper

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Question : 132 of 200

Marks: +1, -0

If

a+ {1}/{b}=b+ {1}/{c}=c+ {1}/{a}(a ≠b ≠c)

then the value of abc is

± 1
± 2
0
± 1/2

Solution:

(1)Let

a+ {1}/{b}=b+ {1}/{c}=c+ {1}/{a}=±1

Let,

a+ {1}/{b}=1 ⇒ a b+1=b

⇒ a b=b-1

b+ {1}/{c}=1 ⇒c= {1}/{1-b}

and therefore,

a b c= {b-1}/{1-b}=-1

Similarly,

a+ {1}/{b}=-1 ⇒a b=-b-1

and

b+ {1}/{c}=-1 ⇒ c= {1}/{-1-b}

So,

a b c= {-b-1}/{-1-b}=1

Hence, ‘abc’ can be ±1

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